Multiscale modeling

Lagrangian methods are based on the concept of describing fluid flows by following the motion of fluid particles. This appears to overcome numerical difficulties associated with large deformations, which are present and difficult to resolve in Eulerian approaches. In MOVEFREE, we investigate three particle methods, Molecular Dynamics (MD), Dissipative Particle Dynamics (DPD) and Smooth Particle Hydrodynamics (SPH) to cover different time and length scales in fluid dynamics. In an MD simulation, interactions between particles (atoms or molecules) are calculated and this seems to be the most appropriate method to study flows at the nanoscale since the assumption of continuous medium, conventionally employed in fluid dynamics, cannot be applied. At these very small scales, a wide range of studies have shown that as channel dimensions decrease, solid wall particles interact with the fluid and control its behavior, such as fluid atom positions, velocity, temperature and transport properties such as diffusion coefficient, shear viscosity and thermal conductivity. On a larger time and/or spatial scale MD simulations become very time consuming and need large computational resources. At these scales, DPD is considered as a simulation method that bridges the gap between atomistic and mesoscopic simulation and has been successfully applied in modeling complex fluids in periodic domains. As far as macroscale methods are concerned, which correspond to practical engineering problems, SPH is employed. The fluid in SPH is considered as a number of moving particles (“chunks” or blobs of matter). The conservation laws of continuum fluid dynamics, in the form of partial differential equations, are transformed into their particle forms by integral equations through the use of an interpolation function that gives the kernel estimate of the field variables at a point. Information is extracted only at discrete points (the particles) and the integrals are evaluated as sums over neighboring particles. Each fluid particle has a constant mass and time-dependent velocity, density, pressure, dynamic viscosity, temperature (as needed). In the SPH framework the governing PDEs describing the system in motion are transformed to a number of ordinary differential equations (ODEs). Towards these directions, in the MOVEFREE framework, we aim to construct a multiscale approach that connects all time and space scales.